What is the etymology of the idiom "To stink/smell to high heaven?"

Shakespeare did utter smells to heaven ... but I am not sure this is the origin of the idiom:

to stink to high heaven. TFD

Etymonline.com says the following:

Old English stincan "emit a smell of any kind; exhale; rise (of dust, vapor, etc.)" (class III strong verb; past tense stanc, past participle stuncen), common West Germanic (cognates: Old Saxon stincan, West Frisian stjonke, Old High German stinkan, Dutch stinken), from the root of stench. Old English had swote stincan "to smell sweet," but offensive sense also was in Old English and predominated by mid-13c.; smell now tends the same way. Figurative meaning "be offensive" is from early 13c.; meaning "be inept" is recorded from 1924. To stink to high heaven first recorded 1963. etymonline

And there are biblical references to 'smells' and 'high heaven':

God directed use of incense in Old Testament worship and the fragrant or detestable aroma, as the case may be, that rose into “high heaven” or before the “nose” of God. Paul Anderson

I am inclined to go with the etymological reference acknowledging there have been smells, good and bad, wafting to the heavens from mankind since ... the beginning.